Answer
Verified
408.9k+ views
Hint: First draw the circuit diagram of the Wheatstone’s bridge and then try to analyse the condition. Try to understand the concept of the bridge and obtain the required balanced condition by using the concept of current flow and voltage division.
Complete step by step answer: the Wheatstone’s bridge works on the principle that where the ratio of the resistances are equal no current flows through the galvanometer. In normal condition the galvanometer is in unbalanced condition that is current flows through the galvanometer. When no current flows through the galvanometer it is known as the balanced condition of the galvanometer.
The Wheatstone’s bridge will be in the balanced condition when the current through the galvanometer is zero.
Current will divide in magnitude to ${{I}_{1}}\And {{I}_{2}}$ to go through resistors P and R.
So, ${{I}_{1}}P={{I}_{2}}R$
When no current flows through galvanometer current ${{I}_{1}}$ will go through P and Q and current ${{I}_{2}}$ will go through R and S.
So, we can write.
${{I}_{1}}=\dfrac{E}{P+Q}$ and ${{I}_{2}}=\dfrac{E}{R+S}$
By substituting these values in the above equation, we get that
$\begin{align}
& \dfrac{E}{P+Q}P=\dfrac{E}{R+S}R \\
& \dfrac{P}{P+Q}=\dfrac{R}{R+S} \\
& P\left( R+S \right)=R\left( P+Q \right) \\
& PR+PS=PR+PQ \\
& PS=PQ \\
\end{align}$
This is the required condition for a balanced galvanometer.
We can also write it as,
$\dfrac{P}{R}=\dfrac{Q}{S}$
i.e. if the ratio of the resistance connected in the circuit in this way is equal then the galvanometer will be in its balanced condition.
Note: In a wheatstone bridge we have two known resistances and two unknown resistances. From these if we put one resistance with some value then we can find out what value of resistance we should put so that the bridge will be in a balanced condition.
Complete step by step answer: the Wheatstone’s bridge works on the principle that where the ratio of the resistances are equal no current flows through the galvanometer. In normal condition the galvanometer is in unbalanced condition that is current flows through the galvanometer. When no current flows through the galvanometer it is known as the balanced condition of the galvanometer.
The Wheatstone’s bridge will be in the balanced condition when the current through the galvanometer is zero.
Current will divide in magnitude to ${{I}_{1}}\And {{I}_{2}}$ to go through resistors P and R.
So, ${{I}_{1}}P={{I}_{2}}R$
When no current flows through galvanometer current ${{I}_{1}}$ will go through P and Q and current ${{I}_{2}}$ will go through R and S.
So, we can write.
${{I}_{1}}=\dfrac{E}{P+Q}$ and ${{I}_{2}}=\dfrac{E}{R+S}$
By substituting these values in the above equation, we get that
$\begin{align}
& \dfrac{E}{P+Q}P=\dfrac{E}{R+S}R \\
& \dfrac{P}{P+Q}=\dfrac{R}{R+S} \\
& P\left( R+S \right)=R\left( P+Q \right) \\
& PR+PS=PR+PQ \\
& PS=PQ \\
\end{align}$
This is the required condition for a balanced galvanometer.
We can also write it as,
$\dfrac{P}{R}=\dfrac{Q}{S}$
i.e. if the ratio of the resistance connected in the circuit in this way is equal then the galvanometer will be in its balanced condition.
Note: In a wheatstone bridge we have two known resistances and two unknown resistances. From these if we put one resistance with some value then we can find out what value of resistance we should put so that the bridge will be in a balanced condition.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE
Fill the blanks with proper collective nouns 1 A of class 10 english CBSE
Which of the following is not a primary colour A Yellow class 10 physics CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths